Natural Resource Analysis

Analysis

Importing libraries

library(dplyr)
library(readxl)
library(tidygeocoder)
library(sf)
library(mapview)
library(RColorBrewer)
library(plotly)

Importing data

data <- read_excel("geo_NCdata.xlsx")

Natural Resource data

nr_data <- select(data, c("City", "Availability of Water", "Agricultural Potential",
                       "Mining Potential", "Tourism Potential", "Environmental Sensitivity",
                       "latitude", "longitude"))

head(nr_data)

## # A tibble: 6 x 8
##   City     `Availability of~ `Agricultural Po~ `Mining Potenti~ `Tourism Potent~
##   <chr>                <dbl>             <dbl>            <dbl>            <dbl>
## 1 Aggeney~              19.2              26.4             70.3             16.2
## 2 Alexand~              34.4              20.1             66.4             54.0
## 3 Askham,~              19.0              32.7             34.3             54.4
## 4 Augrabi~              34.3              45.6             30.7             54.2
## 5 Barkly ~              42.0              56.1             76.5             41.2
## 6 Brandvl~              17.0              23.1             28.1             17.7
## # ... with 3 more variables: Environmental Sensitivity <dbl>, latitude <dbl>,
## #   longitude <dbl>

Distribution Analysis

• Availability of water: Rainfall, Dams, Perennial rivers, Ground water potential, Boreholes
• Agricultural Potential: Crop production / Irrigated land, Grazing Capacity, Agro-processing facilities, Land capability, Aridity zones
• Mining Potential: Active mines, Mineral deposits, Mining applications
• Tourism Potential: Terrain index, Cultural and heritage sites
• Environment Sensitivity: Protected and Conservation Areas, Biodiversity and Geohazards, NFEPA rivers and wetlands.

fig <- nr_data %>%
  plot_ly(
    y = ~`Availability of Water`,
    type = 'violin',
    box = list(visible = T),meanline = list(visible = T), x0 = 'Availability of Water') 
fig <- fig %>%
  layout(
    title = "Distribution of Availability of Water",
    yaxis = list(title = "%", zeroline = F))

fig

Cities/Towns that are not geocoded

nr_data[rowSums(is.na(nr_data)) > 0,]$City

## [1] "Delpoortshoop, Northern Cape"    "Olynvenhoutsdrif, Northern Cape"
## [3] "Phillipstown, Northern Cape"     "Soverby, Northern Cape"

Removing Cities that are not geocoded

locations_nr <- subset(nr_data, !is.na(nr_data$longitude) & !is.na(nr_data$latitude))

K-means Cluster Analysis

• Clustering is a broad set of techniques for finding subgroups of observations within a data set. When we cluster observations, we want observations in the same group to be similar and observations in different groups to be dissimilar. Because there isn’t a response variable, this is an unsupervised method, which implies that it seeks to find relationships between the n observations without being trained by a response variable. Clustering allows us to identify which observations are alike, and potentially categorize them therein. K-means clustering is the simplest and the most commonly used clustering method for splitting a dataset into a set of k groups. In this case, clustering will aid in finding Cities/Towns with similar Natural Resources.

• k-means clustering is a method of vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster.

• Clustering is the process of grouping data objects using a similarity measure.

• Clustering can be hierarchical or partitional, exclusive, overlapping or fuzzy, and complete or partial.

• K-Means is a partitional clustering technique; data objects are divided into non-overlapping groups.

• K-Means is a prototype-based clustering

• A prototype-based cluster is represented by a prototype such that all members within a cluster are close to the corresponding prototype.

• Centroid and medoid are two commonly used prototypes.

• K-Means clustering learns properties of a set of data points and forms partitions called clusters, that represent data with similar properties. For continuous data, each cluster is represented by the centroid which is the mean of cluster members.

Clustering the data

• Cluster Info: https://www.analyticsvidhya.com/blog/2016/11/an-introduction-to-clustering-and-different-methods-of-clustering/
• Cluster Meaning: a group of similar things or people positioned or occurring closely together.
• Cluster Meaning (Statistic): (of data points) have similar numerical values.
• Cluster Meaning (Statistic) example: “students tended to have marks clustering around 70 per cent”

Standardizing data

• Standardizing (scaling) data to remove variations due to different measurement scales

locations_nr_scale <- scale(select(locations_nr,
                                   c("Availability of Water", "Agricultural Potential",
                       "Mining Potential", "Tourism Potential", "Environmental Sensitivity")))

Assessing Clustering Tendency (ACT)

• ACT evaluates whether the data set contains meaningful clusters or not (feasibility of the cluster analysis)
• Method: Statistical (Hopkins statistic)
• The Hopkins statistic is used to assess the clustering tendency of a data set by measuring the probability that a given data set is generated by a uniform data distribution,it tests the spatial randomness of the data.
• A Hopkins statistic(H) value of about 0.5 means that the data is uniformly distributed
• Null hypothesis: the data set D is uniformly distributed (i.e., no meaningful clusters)
• Alternative hypothesis: the data set D is not uniformly distributed (i.e.contains meaningful clusters)
• If the value of Hopkins statistic is close to zero, then we can reject the null hypothesis and conclude that the data set D is significantly clusterable

#hopkins(locations_nr_scale, n = nrow(locations_nr_scale)-1)

Estimating the optimal number of clusters

• Methods: Elbow method (within sum of square) and Silhouette method
• library: factoextra

library(factoextra)

fviz_nbclust(locations_nr_scale, kmeans, method = "wss")

fviz_nbclust(locations_nr_scale, kmeans, method =  "silhouette")

K-means Clustering

• 7 number of clusters will be ideal for grouping observation as shown in the estimation methods above

set.seed(123)

locations_nr_cluster <- kmeans(locations_nr_scale, 
                               centers = 7, nstart = 25)

library(ggplot2)
library(plotly)

Cluster Visual Assessment

• Observations are represented by points in the plot, using principal components if ncol(data) > 2.
• PCA is used in exploratory data analysis and for making predictive models. It is commonly used for dimensionality reduction by projecting each data point onto only the first few principal components to obtain lower-dimensional data while preserving as much of the data’s variation as possible.

ggplotly(fviz_cluster(locations_nr_cluster, data = locations_nr_scale) +
           theme_minimal() +
           theme(legend.position = "none") +
           ggtitle("Natural Resource Clusters (Groups)"))

Adding the clusters to the Natural Resource Data Frame

locations_nr$Cluster <- as.factor(locations_nr_cluster$cluster)

head(locations_nr)

## # A tibble: 6 x 9
##   City     `Availability of~ `Agricultural Po~ `Mining Potenti~ `Tourism Potent~
##   <chr>                <dbl>             <dbl>            <dbl>            <dbl>
## 1 Aggeney~              19.2              26.4             70.3             16.2
## 2 Alexand~              34.4              20.1             66.4             54.0
## 3 Askham,~              19.0              32.7             34.3             54.4
## 4 Augrabi~              34.3              45.6             30.7             54.2
## 5 Barkly ~              42.0              56.1             76.5             41.2
## 6 Brandvl~              17.0              23.1             28.1             17.7
## # ... with 4 more variables: Environmental Sensitivity <dbl>, latitude <dbl>,
## #   longitude <dbl>, Cluster <fct>

Cluster Mean

• Creating a Natural Resource Cluster data frame

nr_clust <- select(locations_nr, c("Availability of Water", "Agricultural Potential",
                       "Mining Potential", "Tourism Potential", "Environmental Sensitivity"))

• Computing the cluster mean the different Natural Resources
• This informs on how natural resources vary by group
• The cluster centers assist in evaluating the distinctness of clusters. Thereby, suggesting whether or not cluster analysis was executed properly

nr_clust_table <- aggregate(nr_clust,
                            by=list(cluster= locations_nr_cluster$cluster),
                            mean)

nr_clust_table

##   cluster Availability of Water Agricultural Potential Mining Potential
## 1       1              24.58120               28.87901         52.73583
## 2       2              39.71313               57.21372         68.73526
## 3       3              34.99344               38.45660         35.36125
## 4       4              24.66475               34.42678         27.20825
## 5       5              33.87909               42.32195         75.05238
## 6       6              35.43283               46.15791         38.63769
## 7       7              20.51299               26.72645         25.11277
##   Tourism Potential Environmental Sensitivity
## 1          41.46333                  31.25629
## 2          25.83522                  37.47207
## 3          22.59556                  42.73840
## 4          28.99601                  63.86612
## 5          15.95009                  58.56706
## 6          53.02939                  37.06212
## 7          53.50389                  42.81456

Natural Resource Clusters

• Plotly default color list: https://stackoverflow.com/questions/40673490/how-to-get-plotly-js-default-colors-list

# locations_nr %>%
#       group_by(Cluster) %>%
#       summarise(n = n()) %>%
#       arrange(n) %>%
#       mutate(Cluster = factor(Cluster, levels = unique(Cluster))) %>%
#       plot_ly(x = ~n, y = ~Cluster, type = "bar") %>%
#       layout(title = "Natural Resource Grouping", yaxis = list(title = "Cluster"),
#              xaxis = list(title = "Number of Cities/Towns"))

ggplotly(locations_nr %>%
      group_by(Cluster) %>%
      summarise(No_of_Cities = n()) %>%
      arrange(No_of_Cities) %>%
      mutate(Cluster = factor(Cluster, levels = unique(Cluster))) %>%
      ggplot(aes(x = Cluster, y = No_of_Cities)) +
      geom_bar(stat = "identity",
               fill = "#1f77b4") +
      geom_text(aes(label = No_of_Cities),
                vjust = -0.25) +
      coord_flip() +
      labs(x = "Cluster", 
           y = "Number of Cities/Towns",
           title = "Natural Resource Grouping (Clusters)") +
      theme_minimal())

Viewing Mapview according to clusters

• SF object of cluster data for Natural Resources

Natural_Resource <- st_as_sf(locations_nr, coords = c("longitude", "latitude"), crs = 4326)

mapview(Natural_Resource, 
        zcol = "Cluster")